Universality in the Vibrational Spectra of Single-Component Amorphous Clusters

Abstract

We have numerically investigated the vibrational spectra of amorphous single-component clusters for several types of interactions among the particles. For all the potentials we have studied, we find that the density of states can be described, except at the two ends of the spectrum, by the same functional form to a very good approximation, and that the fluctuation properties of the spectra in this central region converge to those of the Gaussian orthogonal ensemble of random matrices with increasing system size. We conjecture that this scenario is true for a broad class of potentials.

Spectral statistics of the quenched normal modes of a network-forming molecular liquid

“…[13][14][15][16]26,27 To unfold the data, we define H͑͒ to be the number of frequencies equal to or less than ͑shown in Fig. Unless stated otherwise, the fluctuation properties presented below are computed for the eigenfrequencies, in contrast to earlier studies 13-16 that used the eigenvalues.…”

“…For a particular IS, we denote the elements of the obtained spectra of eigenfrequencies by ␣ with ␣ =1,2, ... ,6N. We also calculate the misfit ͑or residual͒ function [13][14][15] corresponding to the fits in each region to check how well D͑͒ approximates H͑͒. In order to study the fluctuation properties, we first must transform the frequencies in such a way that the average spacing between two successive frequencies in a given spectrum is unity.…”

“…3͑b͒. 13 In Figs. This calculation is extremely sensitive even to very small errors in the approximation to S. The contribution of any such error to ⌺ 2 ͑r͒ grows as r 2 , whereas the GOE prediction for ⌺ 2 ͑r͒ grows only as ln͑r͒.…”

“…[12][13][14][15] For example, random matrix theory has been used extensively for the analysis of statistical fluctuations of the spectra of complex quantum systems such as complex nuclei, quantum chaotic systems, and dis-ordered mesoscopic systems. [12][13][14][15] For example, random matrix theory has been used extensively for the analysis of statistical fluctuations of the spectra of complex quantum systems such as complex nuclei, quantum chaotic systems, and dis-ordered mesoscopic systems.…”

“…[11][12][13][14][15][16] These results have been obtained using the spectra derived from both INM and QNM properties, although the clearest indications seem to have come from using QNM data. [11][12][13][14][15][16] These results have been obtained using the spectra derived from both INM and QNM properties, although the clearest indications seem to have come from using QNM data.…”